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Title: Comparison of spherical harmonics method and discrete ordinates method for radiative transfer in a turbulent jet flame

Abstract

Here, in this study, we systematically compared the accuracy and computational cost of two popular solution methods for the radiative transfer equation (RTE): the spherical harmonics method (PN) and the discrete ordinates method (DOM). We first investigated convergence characteristics of different orders of PN and DOM in a series of 1D homogeneous configurations with varying optical thicknesses. Both solvers perform better for optically thicker cases. The accuracy of PN methods increases with its order, , but the gain in accuracy reduces with the increase in , i.e., improvement of P7 over P5 is less than that of P3 over P1. This decreasing trend becomes more prominent as the optical thickness decreases. On the other hand, DOM’s accuracy increases almost linearly with the increase in the number of ordinates (or polar angles in this study) in all cases. While comparing the directional profile of radiative intensity, both solvers perform better when the radiative intensity is more isotropic. These solvers were then connected with a full spectrum k-distribution (FSK) spectral model and used to perform radiation-coupled simulations of a turbulent jet flame in an axi-symmetric cylindrical domain. Results obtained from P1 to P7 approximations for PN, and 2 x 4, 4 x 4, 4 x 8, 8 x 8 finite anglesmore » for DOM are compared with that from an optically thin model, and a reference solution from line-by-line (LBL) photon Monte Carlo (PMC) method. The choice of radiation solver shows a noticeable impact on the temperature distribution of the flame. The PN solvers lead to slightly higher radiant fractions and the DOM solvers lead to slightly lower radiant fractions than the PMC benchmark solution. Finally, the computational costs of each of these solvers are also reported and an intermittent evaluation / time blending scheme to improve the computational efficiency of radiation solvers in radiation-coupled simulations are also demonstrated.« less

Authors:
ORCiD logo [1];  [2];  [3]; ORCiD logo [1];  [2]
+ Show Author Affiliations
  1. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
  2. Marquette University, Milwaukee, WI (United States)
  3. University of California, Merced, CA (United States)
Publication Date:
Research Org.:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF); Exascale Computing Project
OSTI Identifier:
1906591
Alternate Identifier(s):
OSTI ID: 1908857
Grant/Contract Number:  
AC05-00OR22725; NSF1258635; NSF1756005; 17-SC-20-SC; 1756005
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Quantitative Spectroscopy and Radiative Transfer
Additional Journal Information:
Journal Volume: 296; Journal Issue: /; Journal ID: ISSN 0022-4073
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; radiative transfer; spherical harmonics method; discrete ordinates method; turbulent jet flame

Citation Formats

Ge, Wenjun, David, Chloe, Modest, Michael F., Sankaran, Ramanan, and Roy, Somesh P. Comparison of spherical harmonics method and discrete ordinates method for radiative transfer in a turbulent jet flame. United States: N. p., 2022. Web. doi:10.1016/j.jqsrt.2022.108459.
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Ge, Wenjun, David, Chloe, Modest, Michael F., Sankaran, Ramanan, & Roy, Somesh P. Comparison of spherical harmonics method and discrete ordinates method for radiative transfer in a turbulent jet flame. United States. https://doi.org/10.1016/j.jqsrt.2022.108459
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Ge, Wenjun, David, Chloe, Modest, Michael F., Sankaran, Ramanan, and Roy, Somesh P. Wed . "Comparison of spherical harmonics method and discrete ordinates method for radiative transfer in a turbulent jet flame". United States. https://doi.org/10.1016/j.jqsrt.2022.108459. https://www.osti.gov/servlets/purl/1906591.
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@article{osti_1906591,
title = {Comparison of spherical harmonics method and discrete ordinates method for radiative transfer in a turbulent jet flame},
author = {Ge, Wenjun and David, Chloe and Modest, Michael F. and Sankaran, Ramanan and Roy, Somesh P.},
abstractNote = {Here, in this study, we systematically compared the accuracy and computational cost of two popular solution methods for the radiative transfer equation (RTE): the spherical harmonics method (PN) and the discrete ordinates method (DOM). We first investigated convergence characteristics of different orders of PN and DOM in a series of 1D homogeneous configurations with varying optical thicknesses. Both solvers perform better for optically thicker cases. The accuracy of PN methods increases with its order, , but the gain in accuracy reduces with the increase in , i.e., improvement of P7 over P5 is less than that of P3 over P1. This decreasing trend becomes more prominent as the optical thickness decreases. On the other hand, DOM’s accuracy increases almost linearly with the increase in the number of ordinates (or polar angles in this study) in all cases. While comparing the directional profile of radiative intensity, both solvers perform better when the radiative intensity is more isotropic. These solvers were then connected with a full spectrum k-distribution (FSK) spectral model and used to perform radiation-coupled simulations of a turbulent jet flame in an axi-symmetric cylindrical domain. Results obtained from P1 to P7 approximations for PN, and 2 x 4, 4 x 4, 4 x 8, 8 x 8 finite angles for DOM are compared with that from an optically thin model, and a reference solution from line-by-line (LBL) photon Monte Carlo (PMC) method. The choice of radiation solver shows a noticeable impact on the temperature distribution of the flame. The PN solvers lead to slightly higher radiant fractions and the DOM solvers lead to slightly lower radiant fractions than the PMC benchmark solution. Finally, the computational costs of each of these solvers are also reported and an intermittent evaluation / time blending scheme to improve the computational efficiency of radiation solvers in radiation-coupled simulations are also demonstrated.},
doi = {10.1016/j.jqsrt.2022.108459},
journal = {Journal of Quantitative Spectroscopy and Radiative Transfer},
number = /,
volume = 296,
place = {United States},
year = {Wed Dec 07 00:00:00 EST 2022},
month = {Wed Dec 07 00:00:00 EST 2022}
}
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Works referenced in this record:

Full-scale 3D-modelling of the radiative heat transfer in rotary kilns with a present bed material
journal, February 2020

A comparison of approximate models for radiation in gas turbines
journal, January 2004

  • Frank, M.; Seaid, M.; Klar, A.
  • Progress in Computational Fluid Dynamics, An International Journal, Vol. 4, Issue 3/4/5
  • DOI: 10.1504/PCFD.2004.004087

A model of the cumulative distribution function for wide band radiative properties
journal, June 1998

Further Development of the Elliptic PDE Formulation of thePNApproximation and its Marshak Boundary Conditions
journal, August 2012

Radiative Transfer in Anisotropically Scattering Media: Allowance for Fresnel Reflection at the Boundaries
journal, February 1968

  • Hottel, H. C.; Sarofim, A. F.; Evans, L. B.
  • Journal of Heat Transfer, Vol. 90, Issue 1
  • DOI: 10.1115/1.3597460

Comparison of accuracy and computational expense of radiation models in simulation of non-premixed turbulent jet flames
journal, June 2015

Evaluation of three different radiative transfer equation solvers for combined conduction and radiation heat transfer
journal, November 2016

  • Sun, Yujia; Zhang, Xiaobing; Howell, John R.
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 184
  • DOI: 10.1016/j.jqsrt.2016.07.024

Three-dimensional radiation in absorbing-emitting-scattering media using the discrete-ordinates approximation
journal, January 1988

Evaluation of discrete ordinates method for radiative transfer in rectangular furnaces
journal, January 1997

Numerical simulation of the interaction between turbulence and radiation in reactive flows
journal, August 2007

Note on the Spherical Harmonic Method As Applied to the Milne Problem for a Sphere
journal, April 1947

The impact of radiative heat transfer in combustion processes and its modeling – with a focus on turbulent flames
journal, December 2020

Radiative heat Transfer in Axisymmetric Geometries Using an Unstructured Finite-Volume Method
journal, June 1998

  • Murthy, J. Y.; Mathur, S. R.
  • Numerical Heat Transfer, Part B: Fundamentals, Vol. 33, Issue 4
  • DOI: 10.1080/10407799808915040

Discussion of the Finite-Volume Method for Radiation, and its Application Using 3d Unstructured Meshes
journal, June 1999

Implementation of High-Order Spherical Harmonics Methods for Radiative Heat Transfer on openfoam
journal, May 2015

  • Ge, Wenjun; Marquez, Ricardo; Modest, Michael F.
  • Journal of Heat Transfer, Vol. 137, Issue 5
  • DOI: 10.1115/1.4029546

HITEMP, the high-temperature molecular spectroscopic database
journal, October 2010

  • Rothman, L. S.; Gordon, I. E.; Barber, R. J.
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 111, Issue 15
  • DOI: 10.1016/j.jqsrt.2010.05.001

Application of composition PDF methods in the investigation of turbulence–radiation interactions
journal, April 2002

  • Li, Genong; Modest, Michael F.
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 73, Issue 2-5
  • DOI: 10.1016/S0022-4073(01)00218-7

Effects of radiation model on the modeling of a laminar coflow methane/air diffusion flame
journal, July 2004

The Equations of Radiative Transfer of Energy
journal, November 1917

  • Jeans, J. H.
  • Monthly Notices of the Royal Astronomical Society, Vol. 78, Issue 1
  • DOI: 10.1093/mnras/78.1.28

Finite volume radiative heat transfer procedure for irregular geometries
journal, July 1995

  • Chai, John C.; Parthasarathy, Girija; Lee, HaeOk S.
  • Journal of Thermophysics and Heat Transfer, Vol. 9, Issue 3
  • DOI: 10.2514/3.682

Determination of laminar flame speeds using stagnation and spherically expanding flames: Molecular transport and radiation effects
journal, September 2014

Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium
journal, June 2006

Semi-implicit time integration for thermal radiative transfer
journal, August 2008

  • McClarren, Ryan G.; Evans, Thomas M.; Lowrie, Robert B.
  • Journal of Computational Physics, Vol. 227, Issue 16
  • DOI: 10.1016/j.jcp.2008.04.029

A quasi-Monte Carlo solver for thermal radiation in participating media
journal, February 2020

The interaction between soot and NO formation in a laminar axisymmetric coflow ethylene/air diffusion flame
journal, April 2007

Radiative transfer in three-dimensional rectangular enclosures containing inhomogeneous, anisotropically scattering media
journal, June 1985

  • Mengüç, M. P.; Viskanta, R.
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 33, Issue 6
  • DOI: 10.1016/0022-4073(85)90021-4

Convective and radiative internal heat transfer augmentation with fiber arrays
journal, November 1998

Radiative Transfer in Axisymmetric, Finite Cylindrical Enclosures
journal, May 1986

  • Mengu¨c¸, M. P.; Viskanta, R.
  • Journal of Heat Transfer, Vol. 108, Issue 2
  • DOI: 10.1115/1.3246915

A comparison of specularly reflective boundary conditions and rotationally invariant formulations for Discrete Ordinate Methods in axisymmetric geometries
journal, October 2016

  • Cai, Jian; Roy, Somesh; Modest, Michael F.
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 182
  • DOI: 10.1016/j.jqsrt.2016.05.005

Thermal stability of radiating fluids: The Bénard problem
journal, January 1973

Assessment of narrow-band and full spectrum gas radiation methods in a real industrial glass furnace configuration
journal, November 2022

Robust and accurate filtered spherical harmonics expansions for radiative transfer
journal, August 2010

Two-Dimensional Radiation in Absorbing-Emitting Media Using the P-N Approximation
journal, May 1983

  • Ratzel, A. C.; Howell, J. R.
  • Journal of Heat Transfer, Vol. 105, Issue 2
  • DOI: 10.1115/1.3245583

Improved full-spectrum k-distribution implementation for inhomogeneous media using a narrow-band database
journal, July 2014

Effects of turbulence on species mass fractions in methane/air jet flames
journal, January 1998

Extinction of counterflow diffusion flames with radiative heat loss and nonunity Lewis numbers
journal, February 2007

A Hybrid Wavenumber Selection Scheme for Line-By-Line Photon Monte Carlo Simulations in High-Temperature Gases
journal, July 2013

  • Ren, Tao; Modest, Michael F.
  • Journal of Heat Transfer, Vol. 135, Issue 8
  • DOI: 10.1115/1.4024385

Dynamics of a radiating gas with application to flow over a wavy wall.
journal, February 1966

Finite Volume Method for Radiative Heat Transfer Using Unstructured Meshes
journal, July 1998

  • Murthy, J. Y.; Mathur, S. R.
  • Journal of Thermophysics and Heat Transfer, Vol. 12, Issue 3
  • DOI: 10.2514/2.6363

A full-spectrum k-distribution look-up table for radiative transfer in nonhomogeneous gaseous media
journal, January 2016

  • Wang, Chaojun; Ge, Wenjun; Modest, Michael F.
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 168
  • DOI: 10.1016/j.jqsrt.2015.08.017

Three-dimensional spectral radiative heat transfer solutions by the discrete-ordinates method
journal, July 1991

  • Fiveland, W. A.; Jamaluddin, A. S.
  • Journal of Thermophysics and Heat Transfer, Vol. 5, Issue 3
  • DOI: 10.2514/3.268

Comparison and refinement of the various full-spectrum k-distribution and spectral line weighted-sum-of-gray-gases models for nonhomogeneous media
journal, September 2021

  • Wang, Chaojun; Modest, Michael F.; Ren, Tao
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 271
  • DOI: 10.1016/j.jqsrt.2021.107695

A new radiation solution method for incorporation in general combustion prediction procedures
journal, January 1981

Modelling of radiative heat transfer in enclosures with obstacles
journal, February 1998

  • Coelho, P. J.; GonÇalves, J. M.; Carvalho, M. G.
  • International Journal of Heat and Mass Transfer, Vol. 41, Issue 4-5
  • DOI: 10.1016/S0017-9310(97)00158-0

Comparison of discrete ordinates formulations for radiative heat transfer in multidimensional geometries
journal, January 1995

  • Fiveland, W. A.; Jessee, J. P.
  • Journal of Thermophysics and Heat Transfer, Vol. 9, Issue 1
  • DOI: 10.2514/3.627

Recent advances in the measurement of strongly radiating, turbulent reacting flows
journal, February 2012

  • Nathan, G. J.; Kalt, P. A. M.; Alwahabi, Z. T.
  • Progress in Energy and Combustion Science, Vol. 38, Issue 1
  • DOI: 10.1016/j.pecs.2011.04.001

Two-dimensional axisymmetric formulation of high order spherical harmonics methods for radiative heat transfer
journal, May 2015

  • Ge, Wenjun; Modest, Michael F.; Marquez, Ricardo
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 156
  • DOI: 10.1016/j.jqsrt.2015.01.013

Assembly of full-spectrum k-distributions from a narrow-band database; effects of mixing gases, gases and nongray absorbing particles, and mixtures with nongray scatterers in nongray enclosures
journal, January 2005

  • Modest, Michael F.; Riazzi, Robert J.
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 90, Issue 2
  • DOI: 10.1016/j.jqsrt.2004.03.007

Elliptic PDE formulation of general, three-dimensional high-order -approximations for radiative transfer
journal, March 2007

  • Yang, Jun; Modest, Michael F.
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 104, Issue 2
  • DOI: 10.1016/j.jqsrt.2006.07.017

Prediction of radiative transfer in cylindrical enclosures with the finite volume method
journal, October 1992

  • Chui, E. H.; Raithby, G. D.; Hughes, P. M. J.
  • Journal of Thermophysics and Heat Transfer, Vol. 6, Issue 4
  • DOI: 10.2514/3.11540

Challenges for radiative transfer 1: Towards the effective solution of conjugate heat transfer problems
journal, December 2018

  • Howell, John R.; Mengüç, M. Pinar
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 221
  • DOI: 10.1016/j.jqsrt.2018.10.016

Development of high-order P models for radiative heat transfer in special geometries and boundary conditions
journal, March 2016

  • Ge, Wenjun; Modest, Michael F.; Roy, Somesh P.
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 172
  • DOI: 10.1016/j.jqsrt.2015.09.001

The rank correlated FSK model for prediction of gas radiation in non-uniform media, and its relationship to the rank correlated SLW model
journal, July 2018

  • Solovjov, Vladimir P.; Webb, Brent W.; Andre, Frederic
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 214
  • DOI: 10.1016/j.jqsrt.2018.04.026

Analysis of Discrete Ordinates Method with Even Parity Formulation
journal, April 1997

  • Liu, J.; Shang, H. M.; Chen, Y. S.
  • Journal of Thermophysics and Heat Transfer, Vol. 11, Issue 2
  • DOI: 10.2514/2.6230

Impact of radiation models in CFD simulations of steam cracking furnaces
journal, November 2007

High temperature gas radiative property parameters of statistical narrow-band model for H2O, CO2 and CO, and correlated-K model for H2O and CO2
journal, March 1997

Elliptic PDE formulation and boundary conditions of the spherical harmonics method of arbitrary order for general three-dimensional geometries
journal, June 2008

  • Modest, Michael F.; Yang, Jun
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 109, Issue 9
  • DOI: 10.1016/j.jqsrt.2007.12.018

Line-by-Line Random-Number Database for Monte Carlo Simulations of Radiation in Combustion System
journal, November 2018

  • Ren, Tao; Modest, Michael F.
  • Journal of Heat Transfer, Vol. 141, Issue 2
  • DOI: 10.1115/1.4041803

The Full-Spectrum Correlated-k Distribution for Thermal Radiation From Molecular Gas-Particulate Mixtures
journal, June 2001

  • Modest, Michael F.; Zhang, Hongmei
  • Journal of Heat Transfer, Vol. 124, Issue 1
  • DOI: 10.1115/1.1418697

Assessment of the Finite-Volume Method and the Discrete Ordinate Method for Radiative heat Transfer in a Three-Dimensional Rectangular Enclosure
journal, February 1999

  • Seung H. Kim, Kang Y. Huh,
  • Numerical Heat Transfer, Part B: Fundamentals, Vol. 35, Issue 1
  • DOI: 10.1080/104077999276027

Solution of the Radiative Transfer Equation in Three-Dimensional Participating Media Using a Hybrid Discrete Ordinates: Spherical Harmonics Method
journal, September 2012

  • Sankar, Maathangi; Mazumder, Sandip
  • Journal of Heat Transfer, Vol. 134, Issue 11
  • DOI: 10.1115/1.4007129

Use of Discrete-Ordinates Methods for Solution of Photon Transport Problems
journal, April 1966

The HITRAN2012 molecular spectroscopic database
journal, November 2013

  • Rothman, L. S.; Gordon, I. E.; Babikov, Y.
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 130, p. 4-50
  • DOI: 10.1016/j.jqsrt.2013.07.002

Simplified PN Approximations to the Equations of Radiative Heat Transfer and Applications
journal, December 2002

  • Larsen, Edward W.; Thömmes, Guido; Klar, Axel
  • Journal of Computational Physics, Vol. 183, Issue 2
  • DOI: 10.1006/jcph.2002.7210

A Finite-Volume Method for Predicting a Radiant Heat Transfer in Enclosures With Participating Media
journal, May 1990

  • Raithby, G. D.; Chui, E. H.
  • Journal of Heat Transfer, Vol. 112, Issue 2
  • DOI: 10.1115/1.2910394
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